Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Sat, 5 Apr 2025 16:03:18 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <0d7e70842fd4f479836f288d42e65d9e583b3b2c@i2pn2.org>
References: <vrfvbd$256og$2@dont-email.me>
 <215f3f8823df394f0cbd307af57a528cb3afc52f@i2pn2.org>
 <vsc6lj$27lbo$1@dont-email.me>
 <ba194532a2343e7068ed57b756a99f48241a94fb@i2pn2.org>
 <vsce69$2fv3s$1@dont-email.me>
 <7e0f966861ff1efd916d8d9c32cc9309fd92fe82@i2pn2.org>
 <vsckdc$2l3cb$1@dont-email.me>
 <cd467496ff18486f746047b3b1affc4927981c0c@i2pn2.org>
 <vsct12$2ub5m$1@dont-email.me>
 <3ab00594a6cdaa3ca8aa32da86b865f3a56d5159@i2pn2.org>
 <vsd1p9$379dn$3@dont-email.me>
 <45167877871179050e15837d637c4c8a22e661fd@i2pn2.org>
 <vsenb0$th5g$7@dont-email.me>
 <4c1393a97bc073e455df99e0a2d3a47bfc71d940@i2pn2.org>
 <vsfe66$1m8qr$4@dont-email.me>
 <7286761fb720294d7a87d883fc82c8f8cf95a460@i2pn2.org>
 <vsfl7f$1s8b0$3@dont-email.me>
 <6edcdf0fa4f6ec503240b27a5801f93c470ed7d6@i2pn2.org>
 <vsh931$3mdkb$1@dont-email.me> <vsivgk$1fjla$1@dont-email.me>
 <vsjmtj$26s7s$2@dont-email.me> <vslbsr$1uta$1@dont-email.me>
 <vsmlq3$1bbrc$1@dont-email.me> <vsqm6m$1msj7$1@dont-email.me>
 <vsrqi8$2rgr9$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sat, 5 Apr 2025 20:21:14 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="3280877"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
Content-Language: en-US
In-Reply-To: <vsrqi8$2rgr9$2@dont-email.me>
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 4588
Lines: 63

On 4/5/25 1:51 PM, olcott wrote:
> On 4/5/2025 2:30 AM, Mikko wrote:
>> On 2025-04-03 18:59:15 +0000, olcott said:
>>
>>> On 4/3/2025 2:03 AM, Mikko wrote:
>>>> On 2025-04-02 15:59:47 +0000, olcott said:
>>>>
>>>>> On 4/2/2025 4:20 AM, Mikko wrote:
>>>>>> On 2025-04-01 17:51:29 +0000, olcott said:
>>>>>>
>>>>>>>
>>>>>>> All we have to do is make a C program that does this
>>>>>>> with pairs of finite strings then it becomes self-evidently
>>>>>>> correct needing no proof.
>>>>>>
>>>>>> There already are programs that check proofs. But you can make 
>>>>>> your own
>>>>>> if you think the logic used by the existing ones is not correct.
>>>>>>
>>>>>> If the your logic system is sufficiently weak there may also be a 
>>>>>> way to
>>>>>> make a C program that can construct the proof or determine that 
>>>>>> there is
>>>>>> none.
>>>>>
>>>>> When we define a system that cannot possibly be inconsistent
>>>>> then a proof of consistency not needed.
>>>>
>>>> But a proof of paraconsistency is required.
>>>
>>> When it is stipulated that {cats} <are> {Animals}
>>> When it is stipulated that {Animals} <are> {Living Things}
>>> Then the complete proof of those is their stipulation.
>>> AND {Cats} <are> {Living Things} is semantically entailed.
>>
>> For that sort of system paraconsistency is possible, depending on
>> what else there is in the system.
>>
> 
> https://en.wikipedia.org/wiki/Paraconsistent_logic
> Starting with a consistent set of basic facts (AKA axioms)
> while only allowing semantic logical entailment thus
> truth preserving operations does not seem to allow
> any contradictions, thus paraconsistency.
> Try to provide a concrete counter-example.
> 

Your problem is you are making the error of assuming the concluion.

You can't tell that you axioms ARE consistant excpet by proving that the 
system itself is consistant, which has been shown can't be done in the 
system if the system has the needed power. The question has always been, 
how to PROVE that the axioms we started off with were consistant within 
the system itself.

Note, that paraconsistant system are paraconsistant because they weaken 
the power of the classical logic inference. One effect of that is they 
don't support the needed properties of the Natural Numbers.

paraconsistant systems can support limited inconsistant axioms without 
going all inconsistent, but that inconsistancy might be limited in 
extent in the system. This sort of logic, as that article states, is to 
allow coming up with some conclusions when the input data (the axioms) 
might not be fully consistant.